According to this article on Fortune.com, although Amazon Web Services still dominates the public cloud market, Microsoft is making ground and closing the gap.
They cite a survey featuring input from 1060 cloud customers:
Overall, AWS is used by 57 percent of respondents, flat from last year. Enterprise adoption of AWS grew from 50 percent to 56 percent while adoption by smaller businesses fell slightly from 61 percent to 58 percent. Azure IaaS grows strongly from 12 percent to 17 percent adoption, while Azure PaaS grows from 9 percent to 13 percent.